Commando/thong always makes me nervous after hearing about somebody's pants getting ripped when their horse rubbed their (horse) head against the person and the curb chain hook split her pants. Standing right outside the ring among everybody..
Hanky Panky. I wear these 80% of the time. They are hands down the most comfortable underwear I've worn in my life. They're great for riding and during heavy work outs.
Don't be fooled by the VS or la senza imitators. They look similar to the HP only they're half as comfortable.
To avoid VPL AND boot rubs behind the knee, as well as provide a bit of flattering compression that my middle-aged middle needs, I wear capri-length body shapers. Smartpak makes "smart slim", which are pretty good, but not my favorite. The ones I love are Flexees. I thought they'd be too warm for summer, but nope (and I wilt when I get hot). No bunching, rubbing, etc. at all.
I love Hanky Panky, but this brand is my new favorite. Found them through a friend when we were discussing hiking gear, and holy cow I love riding in these. Even if a panty line is visible, I don't care because they're so comfy. So dang easy to clean, too!
The VS no-shows are a lifesaver! I've got a boyshort style and a "cheeky" style, and they're amazing. Bonus is that the boyshort style comes in a range of nude colors, so no matter what your skintone is, you can find no-show panties that also don't show under whites
I've heard there's more to life than an FEI tent and hotel rooms, so I'm trying it.
Jockey underwear in general is very comfortable for riding, and I have not had much trouble with lines even with the regular "bikini" kind, even though just looking at them they look like they would cause line problems.